Question

The owner of an antique store estimates that there is a 20% chance she will make $1600 when she sells an antique china cabinet, a 75% chance she will make $800 when she sells the cabinet. and a 5% chance she will break• even wnen shesells the cabinet. Determine the expected gain or loss for the store.The expected gain or loss for the store is

Answer 1

We need to find the expected gain or loss for the store.

This corresponds to the expected value of the variable x with the following possible values and probabilities:

x 1600 800 0

p(x) 20% 75% 5%

We know that the expected value is the sum of the products xp(x), for all possible values of x.

Thus, we obtain:

`\begin{gathered} 1600\cdot20\%+800\cdot75\%+0\cdot5\% \\ \\ =1600\cdot(20)/(100)+800\cdot(75)/(100)+0 \\ \\ =16\cdot20+8\cdot75 \\ \\ =320+600 \\ \\ =920 \end{gathered}`

Answer

The expected gain for the store is $920.